Seminar: Monotonicity of the Hawking energy and time-flat surfaces

Marc Mars

Monday September 8, 12:00-13:00

The Hawking energy is a functional on spacelike surfaces that is potentially interesting to address the general Penrose inequality. The variation formula for the Hawking mass under a general spacetime deformation will be reviewed and various conditions ensuring monotonicity will be discussed, with special emphasis on the time-flat condition recently introduced by Bray and Jauregui. The preservation of the time flat condition along the flow will be addressed and rigidity results for time flat surfaces in static spacetimes will be presented.